\subsection{Syntax}
The following table summarizes the various operators and expression syntax.
The arithmetic operators have the expected precedence, that is,
multiplication and division are evaluated before add and subtract.
Subexpressions surrounded by parentheses have highest precedence.

\begin{center}
\begin{tabular}{clll}
{\it Math} & & {\it Eigenmath} & {\it Comment} \\
\\
$a=b$ & & \verb$a == b$ & {\it test for equality} \\
\\
$-a$ & & {\tt -a} & {\it negation} \\
\\
$a+b$ & & {\tt a+b} & {\it addition} \\
\\
$a-b$ & & {\tt a-b} & {\it subtraction} \\
\\
$ab$ & & {\tt a b} & {\it multiplication, alternatively,} \verb$a*b$ \\
\\
$\displaystyle\frac{a}{b}$ & & {\tt a/b} & {\it division}\\
\\
$\displaystyle\frac{a}{bc}$ & & {\tt a/b/c} & {\it division operator is left-associative} \\
\\
$a^2$ & & {\tt a{\char94}2} & {\it power}\\
\\
$\sqrt{a}$ & & \verb$sqrt(a)$ & {\it square root, alternatively,} \verb$a^(1/2)$ \\
\\
$a(b+c)$ & & {\tt a (b+c)} & {\it with a space in between, alternatively,} \verb$a*(b+c)$ \\
\\
$f(a)$ & & {\tt f(a)} & {\it function evaluation} \\
\\
$\begin{pmatrix}a\\ b\\ c\end{pmatrix}$ & & {\tt (a,b,c)} & {\it vector} \\
\\
$\begin{pmatrix}a&b\\ c&d\end{pmatrix}$ & & {\tt ((a,b),(c,d))} & {\it matrix} \\
\\
$F^1{}_2$ & & {\tt F[1,2]} & {\it tensor component access} \\
\\
-- & & \verb$"hello, world"$ & {\it string literal} \\
\end{tabular}
\end{center}
